# Georeferencing: Rubbersheet with Control Points

Last Updated: May 5, 2017

### How to Georeference an Image with Control Points

You can take any drawing, any schematic and put that image into geographic context.

When you take any ordinary image and give it real-world coordinates, you are georeferencing it.

You can stretch, scale, rotate and skew the image to better relate to physical space. You can even take it a step further and vectorize those features and query them.

If you’re in need of learning how to georeference, it’s really 3 easy steps.

• Select a transformation or rubbersheeting method.

Follow this georeferencing tutorial on how to georeference with precision.

### Add Control Points for Matching Locations

How do you put any image into geographic context?

You’ll need to find something that already has real-world coordinates. In other words, you need anything that is georeferenced already.

You then use it as the reference image for control points. Control points are specific locations commonly found in two images.

Do yourself a favor and find the most suitable image as possible. For example, if you want to georeference an aerial photo taken in 1920, you should use a reference image closest to that date for better control points.

Once you find that reference image, it’s then a matter of finding matching targets in both scenes.

• Click on a specific location in the first image you want to georeference.
• Next, click on the reference image matching location.
• Repeat until you have four (preferably more) control points.

In the end, your image will have the coordinate system that’s set in your data frame.

While there’s no perfect number of control points, it completely depends on the scan of your image and RMSE.

### Rubbersheeting (Polynomial) vs Affine Transformation

When you are georeferencing, you stretch, scale, rotate and skew the image to better relate it to physical space.

Generally, an affine transformation is sufficient for georeferencing. An affine transformation preserves straight lines in two-dimensional space by scaling, rotating, translating and skewing the image.

Alternatively, rubbersheeting gives more flexibility by bending and warping images through a third order polynomial equation. A higher polynomial allows more bending and warping of an image.

Although a third order polynomial may be useful if there is significant distortion in the scanned image, you will typically use affine transformations for georeferencing.

### Root Mean Square Error (RMSE)

A good rule of thumb is that a low RMSE means a better georeferenced image.

However, a low RMSE does not necessarily mean that your image is fitted on the Earth’s surface any better.

READ MORE: What is Root Mean Square Error (RMSE)

As you add more control points, the RMSE measures how well these control points fit that particular affine or polynomial equation.

$RMSE = {\sqrt {\frac{1} {N}{\sum\limits_{i = 1}^N {(x_{i} - \hat{x}_{i} } })^{2} } }$

When you change the transformation method, you’ll see that higher polynomials lowers your RMSE value. This is because those control points can better fit that equation to mathematically stretch your image into two-dimensional space. But when you inspect your image, it warps in areas where you have less control points.

Overall, if your scan is high quality such as a mylar, then you should select a simple affine transformation.

### Georeferencing: Now, You Try

It’s time to take the training-wheels off.

You have all the core knowledge to georeference with precision.